Overview
This lesson covers how to solve routine and non-routine word problems involving division of fractions or mixed fractions, including identifying appropriate strategies and terms used in such problems.
Key Concepts in Division of Fractions
- Division problems often use terms like quotient, divided by, cut, average, and split into.
- To divide fractions, change the division sign to multiplication and use the reciprocal of the divisor.
- Always convert mixed numbers to improper fractions before dividing.
Translating Word Problems (Learning Test 1)
- "Quotient" indicates a division operation.
- "Divided by," "split into," and "average" also require division.
- Parentheses in expressions indicate multiplication or division must be performed before other operations.
Solving Routine Problems (Learning Test 2)
- Convert whole numbers and mixed fractions to improper fractions before dividing.
- Multiply by the reciprocal of the divisor.
- Simplify results and convert improper fractions to mixed numbers when possible.
- Examples covered: dividing quantities among groups, finding possible output (e.g., number of cakes, pieces of pizza, plastics needed).
Solving Non-Routine Problems (Learning Test 3)
- Apply the same fraction division strategy in more complex or less direct scenarios.
- Scenarios include determining number of portions, cuts, or conversions given specific quantities.
- Steps: convert, multiply by reciprocal, cancel common factors, simplify, and label answers with units.
Self-Assessment (Learning Test 4)
- Reflect on abilities to: identify given info, determine required operation, solve for division of fractions, label answers correctly, and simplify answers.
- Respond with "agree," "disagree," or "more" (if assistance is needed) for each statement.
Key Terms & Definitions
- Quotient — the result of division.
- Reciprocal — a flipped fraction; for a/b, the reciprocal is b/a.
- Improper Fraction — a fraction where the numerator is greater than or equal to the denominator.
- Mixed Fraction — a whole number combined with a proper fraction.
- Cancel (in fractions) — reduce common factors in numerator and denominator before multiplying.
Action Items / Next Steps
- Answer the self-assessment in Learning Test 4, marking agree, disagree, or more as needed.
- Practice translating and solving word problems involving division of fractions.
- Write answers with correct labels and in simplest form.